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Proving the Heine-Borel Theorem with real induction! #SoME4

YouTubeIntercontinentalBallisticMath

Proving the Heine-Borel Theorem with real induction! #SoME4

Heine–Borel from Real Induction | #SoME4 The Heine–Borel theorem says that a subset of the real numbers is compact if and only if it’s closed and bounded. In 100 seconds, we prove the “[a,b] ⇒ compact” direction using real induction — the same technique from our #SoME4 contest entry. This can be generalized (with a little work) to ...

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